Tempered Mittag-Leffler noise-induced resonant behaviors in the generalized Langevin system with random mass

Abstract

In this study, we propose the fluctuating-mass generalized Langevin equation (GLE) with a tempered Mittag-Leffler (M-L) noise, and investigate the generalized stochastic resonance (GSR) phenomena in terms of output amplitude amplification. Based on numerical results, we study the dependence on various parameters systematically, and further discuss the interplay between memory exponent, memory time and tempering parameter, which diversifies the stochastic multi-resonance (SMR), including double-peak GSR, triple-peak GSR and quadruple-peak GSR. It is worth emphasizing that the latter two SMR phenomena have not been observed in the GLE with tempered fractional Gaussian noise. Moreover, as a generalization with tempered M-L noise, the conventional GLEs with M-L memory kernel, power-law memory kernel, or exponent-form memory kernel, can be effectively derived as the special cases of tempered M-L memory kernel. Thus, these results also provide more extensive support for manipulating the GSR behaviors through system parameter control in the potential applications.